Given two colorings \(S_i\)  and \(S_j\) , we use the set-theoretic partition distance \(D(S_i,S_j)\)  to measure the dissimilarity between \(S_i\)  and \(S_j\) , which corresponds to the minimum number of vertices that need to be displaced between color classes of \(S_i\)  to transform \(S_i\)  to \(S_j\)  [1]}. The exact partition distance between two solutions can be calculated with the Hungarian algorithm [2]} in \(O(|V| + n^3)\)  time. However, given that we need to compute millions of distances at each generation with the large population, we instead adopt the efficient approximation algorithm presented in [1]}, which scales in \(O(|V|)\) .
